You need to prepare a 0.165 times 10^3 m diameter tungsten wire with a resistanc

Question

You need to prepare a 0.165 times 10^3 m diameter tungsten wire with a resistance of 3630 Ohm How long must the wire be? The resistivity of tungsten is 5.62 times 10^-8 ohm middot m. The maximum allowed power dissipation for a 22.1-Ohm resistor is stated to be 10.0 W. Find the largest current that this resistor can take safely without burning out. Two resistors, of R_1 = 2.63 Ohm and R_2 = 6.27 Ohm, are connected in series to a battery with an EMF of 24.0 V and negligible internal resistance. Find the current I_1, through the first resistor and the potential difference Delta V_2 between the ends of the second resistor.

Explanation / Answer

(1) R = rho L / A

A = pi d^2 / 4 = pi (0.165 x 10^-3) / 4 = 2.138 x 10^-8 m^2

putting in,

3630 = (5.62 x 10^-8) (L) / (2.138 x 10^-8)

L = 1381.1 m

(2) P = I^2 R

10 = I^2 (22.1)

I = 0.67 A

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